benchmarks.wiki / Public workspace
..······.......···········...........···:::::::::::::::···········::::::::::::::::::::::----=========--:::::·······.
........ ..............······::::::::·······························:::---:::::::::::------::::·····........
........·········............................. .···--------::::::············............
..··---------:::·······.........
..··--=====---::···..........
..··-===++===--:··....
..·:==++++++==-::·...
..·:=++*****++=-:··..
...·:=+**####*++=-:·... ..
..········... ........ . ...··:::::::···......··:=+*##%%##*+=--:·... ..........
..··::::::··. ..·::::::··... ..·:-==+*****+==-::······-=+*#%%%%%#*+=-:··........·······...
..··::::··. .·:-=+**++=-:··......·:-+*%@@@@@@@%*+=-:::::--=+*#%@@@@%#*+=-:··....···:::---::··..
..... ............······::::::---::::::::::················::::::::::::::::--==++*###%%###**++===++****+=-:·.
......····::::::::::::::····················..........·····::::::::---==+++*****+++==---==+++===-:·.
.........············....... ............... ···::::::::::---=========---::::-------:·.
.··::::::::::::::-------::::····:::::::··.
.··:::::::········::::::·····...········..
.··----:::··············.................
..··-----::···..............
..·:====--::··....
...::=====--::·...
...····... ......... ...···::::::···..........:::+++++==-:··..
..······.. .··::--:::··.. ..·::-=+******++=-::······:::+*****+==-:··.. ........
..····.. .·:-=+**++=-::·....··:-+*%@@@@@@@@%#*+=--::--==+**####*++=-:·... ....·······....
.....····::::----------::::::::·················:::::-----:::::---=++*#%@@@@@@@@@%##*****##%@@%#*+=-:·.
......····::::--------:::·····.........................··········:---==+**#%@@@@@@@%%#***++**#%@@%#*+=-:·.
.............·············..... ...... ....···::--==++*##%%@@%%##**++++++*#%@%#*+=-:·
..··:::---==++**#####**++======++*##**+=-·.
··:::::---==+++++++++==-------=++++==-:·.
··::::::::----=====---:::::::::-----::·..
··:::·····::::::::::::··········:::···..
..··:::·················.................
...··:::····............... ......
....... ....·..... . ...··········.... ...···-:::··....
...··.. ..·::----::··........·:--=++***++=--:··......····::=---::··.. .........
...··.. .·-=+****+=-::··..··:-=+#%@@@@@@@%#*+=-::··:::--=======-::·.. ......····.......
....····:::-----==------:::::::::··············:::---=======------==+*#%@@@@@@@@@@@%#*++=++**#@@@@@%#*+=:·.
.....·······::::--------:::····......................·····::::::::··:::=+*#%@@@@@@@@@@@%#**++++*#%@@@@@%#*+=:·.
..............············..... .............:::++*#%@@@@@@@@@@%##*+++**#%%@@@@%#*+=:·.
...::=+*##%@@@@@@@@@%#**++++**#%%@@@%#*+-:..
..·:==+**#%%@@@@@%%#**++===+++*##%%#*+=:·.
..··-==++**#######**++==----===++**++=-:·.
..··----==+++++++++==--:::::::---==--::·..
..··:::::-----------::··········:::::··...
··:·······:::::·····..........·······...
..... ...····.... .......·...... ··.·····.........................····....
....... .·::-----::··.. ..··::--===--::··.... .....······:···.... .............·····....
...... .·:-++****+=-:··....··:-=+*##%%##*+=-:···....···::-----::··... ....··············....
...·····:::-----===--------:::::::::::::···::::--==++*****++==------==+*#%@@@@@@@%#*+=-::::--=*#%@@@@@@%#+-:..
....·······:::::-----::::·······....··.........····:::--------:::::::::--#%@@@@@@@@@%#*+==---==+*%@@@@@@@%#+-·.
..............········...... .....................-==%@@@@@@@@@@%#*++===++*#%@@@@@@@%*=:·.
..·==%@@@@@@@@@@@%#*++++++**#%@@@@@@#+-:·.
.·-=%@@@@@@@@@@@%#*++===++**##%%%%#*=:·.
..--#%%@@@@@@@%%#*++=======+++****+=-:·.
..:-**##%%%%%##**+==---:::---======-:··..
..::=++++***+++==--:::·····::::----:::··..
...··-----------:::············::::::::···..
... ....····.... . ..... .....···::··············.....······::::::::···.
...... ..·::-----::·.. ...····:····... .....······..···..............··········::::::::···..
...... .·:-=+***++=-:·.. .··:--=====--::·.... ....··::::::::··... ....··::::::::::::::····....
....··::::---------------==========-----::---==+**##%%##*+=--:·····::-=+*##%%##*+=-:·.....·:-=*#%@@@@@@%#+-·..
.....·····::::::::::::::·····:::::::··········::---=======--::·······::-==%@@@@%%#*+=-::··::-=+*%@@@@@@@%*=:·.
...............................................··········..........··=++@@@@@@%#*+==-----=+*#%@@@@@@%#+-·.
···+*@@@@@@@@%#*+==-===++*#%%%%%#*+=:·.
··+*@@@@@@@@%#*++======++***#***+=-:..
··+*@@@@@@@@%#*+==------===++++==--:·..
··=+@@@@@%%##*+==--:::::-----===---::···..
··-=#####**++==--:::···:::::----====--::··.
...::======----:::·······::::----======--:·.
........... . ...........···::::::···········:::::::-----====--::·.
...... ..··::---::··.. ........... .....·········...··........····:::::-----::::::::::::··..
...... .·:-==+++==-:·.. ..··::::::··... ....··:::::::::··... ...··::---===---::···..........
..··::---------=====++***####**++==------==+*###%##**+-:·.. .·:-==++++==-:·.. ..·:=+#%@@@@@@%*+=:·.
....···::::::::::::::------------::::::::::--===++===-::·... ..··:--==##**+=-:··...··:-+*#%@@@@@%*+=:·
........................··...............··········.... ...···+++@%%#*+=-::::::-=+*##%%%%#*+-:·.
·::**@@@%#*+==------==++*****+=-:·.
::**@@@@%#*+==-------===+++==--:··..
::**@@@@%#*+==--:::::----====----:::·····..
·:++@@%##*+==--::::::::----======++===--:·..
··==#**++==--:::::::::----===+++**#**+=--:·.
...::===----:::::::::-----====++++***++=-:·.
........... . ..................···:::::::::::------------------===--::·..
...···:::::··... ........... ......·············..........···::--======---::·············..
.... ..··:--===--::·. ..·······..... ....··:::-----:::··... ..··:--===+===-::·.. .......
..·::------====++**#%%%@@%%##*+=--::::--==+*****++=:·. ..·:-====--:·.. ..·-=+#%@@@@@%#+=:·.
..···:::::::::---===++++++==--:::·····::---====--::·.. .··::-----+=-:··....··:-=+*#%%%%#*+-:.
.............···············...........·········... ...·····===*+=-::····::-==+****++=-:·.
:::++#*++=-:::::::--======--:··. ..
::*+%#*+=--:::·::::---------::::··::::::··.
::++%#*+=--:::··::::----=======+++*+++=--:·.
··==**+==--:::::::---===+++***###%%%#*+=-:.
··--+==------------====++++***###%%#*+=-:·.
...:·---------=================++++++=-::·.
............ . ....................... ...·::::--===++++===--:::·····:::-:::··.
...···::::···... .....................·····::::::····..... ...··::-==++++==-::·.. ..·····...
..·:::-----::·.. ...·······..........··::---====--::··.. ..··:--==+++=--:·. .··:::··.
.··:::-----==++*##%%@@%%#*+=-:··...··::-==++++=-:·. .·:-====--:··.. ..·:-=+*#%@%%#*+-:.
..···:::::::--===+++++++=--:···....···::------:··. ..·::------::::··...··::-=++***+=-:·.
..........······:::::····.............······.... ...·······--:-::······::---==---:··. ..···.
···--=-::·······::::--:::::·······::-----:··.
··--=-::········:::----======+++**#**++=-:·.
··--=--:::::::::--===+++***##%%%@@@%#*+-:·.
·.-:=---------====+++****###%%%@@@@#*+-:·.
..::=======+++++++++++++++++*******+=-:·.
...··--==++++**+++==---:::::::---===-::·.
.............. .......... · ....................... ..·:--==++++++==-:··.. ...··::-::··.
...··:::::···... .......................···:::::::::···... .·::-==++++=--:·. .·::---:··.
..·::----::··.. ..·········........···:--==+++==--:·.. .··:-==++==-::·. ..·:-===--:·.
...····:::-==+*#####*+=-:·.. ..·:-=====--:·. .·:-==+++==-::··.....·::-=+****+=-:·. ......
.....···:::--===+===--:··.. ..··::::-::··.. ..·::------::··.·.....··::------:··. .··::::·.
.......············.... .....··..... ...········..··.·.......···:::::····.....··::-=====--:·.
...·.·.......··::::------====++**##%#*+=-:·.
..··:······:::--==+++***###%%%@@@@@%*+=:·..
..:·-------===+++****###%%%@@@@@@%%*+-:·..
..::==+++++******+++++****#######**=-:·.
..::++********++==--------===++++==-:·.
...::++*****++=--:··......··::---==-:··.
....····............................ · .........·····...... .··-=+++++==-:·.. ..·:--===-:·..
..··::::::··.... ......·····...........···:::-----:::·... .·:-==++==-:··. .·:-==++=-:·.
..··::---::·.. ..··::::::::···.....··::-==+++++=-:··. .·:-=+++++=-:·. .·:-=+***+=-:·.
..·::-=+++++=-:·.. .·:--====--:·. .·:-=+***++=--:··.....···::----::·.. .·:--==--:·.
..··::-------:··.. ..··::::::··.. .··:--===--::··.. ...·········.........·::-=+**++=-:·.
....·······.... ........... ....·······.... ...···:::::-------==+++**####*+=-:·.
....···:::--===+++***###%%%%%%%%#*+=::·.
..··:----==++++***####%%%@@@@@%%##*=-:·..
..:-+++***************###%%%%##**+=-:·..
··-=#####***++====--===+++*****+==-:·.
.·-=####**+=--:·······::--==+++==-:·..
...--***++=--:·.. .··:--=====-:·..
.....···........ ............ .·.....········.... ·::++++=--:·. .·::-==++==-:·.
..··::::···.. ...···········.......···::------::··. .··==+++==-:·. .·:-==++++==:·.
..··:::··. .··:--=====--::··....··::--=====-::·. .·:=+*****+=-:·. .·:-=++***+=-·..
.·:--===--:·.. .·:-==++==-:·. .·:-=+*****+=-::·.. ...·······.... ..··:-=++***+=-:··.
..·:::::::··.. ..··::::::··.. ..·::------::··.. ...···::::::::::---==+++*****+==-:·.
....····.... ........... .....···...... .···::---===++++*****######***+=-:··..
··---===++++***####%%%%%%%##**+==-:··..
..--+*************####%%%%%##*++=-:··...
··==###***+++=====++***####**++=-::·...
··==##**+==-::::::--==++****++=--:·...
··==**+=--:·......··:--=++++++=-::·..
..·--++=-:··. .·:--=+++++=--:·..
.......... ....................:..·······.... ...---++=-:·. .·:-=+++++==-:·.
...··.... ..··::::-::::···......····:::::::·.. ..·::--**++=-·.. .·:-=+++++==-:·.
...... .·:-=+**##**+=-:·.. ...··::---::··. .·:-=**####*+-:·. .·:-=+++*++=-:·.
.·:--==--:·.. ..·:-==+++=-::·. ..·:-=++**++=--:·. ...············::::--==++++++++=-:··.
.··::::···.. ..··:::::::··.. ..··::::::::··... .··:::----======+++++++++++++===-:··..
.......... ........... ............. ···--====++++*****#####***+++==--::··...
...--++++++++****#########**++=--::··.....
··==***+++++++++**#######**+=--::··.......
··==*++==------==++**####**+=--:···........
··=-+==-::····::--=+**###**+=--:···........
··--=-::·......··:-=+******+=--:···........
···-:=-:·.. ..·:-=+*****+=--:··.........
.....·····....... ....:........ ...···---=-:·. .·:-=++****+=-::·..........
.··:--======-::·... ...·······.. .··:--===-+=-:·. .·:-=+****+=-:··... ......
.:-=*#%@@@%#*+-:·. .··::--::··. .·:-=+*#####*+-:·. .·:-=++**++=-:·.. ....
..·:----:·.. .·::-=++++==-:·.. ..·::-=====--::·.. ...···::::-----------============---:·..
..··:::··.. ...··:::::::··... ...···::::····............···----======+++++++++++===---::::··...
......... ........... ..........................:::====+++++*********++==--:::····....
···--++===++++***#####**++=--:····.......
··--+=======++***#####*++=--:····.·.......
··-:=--:::---=++*######*+==-:···········...
··::-::····::-=+**#####**+=-::············.
·.:·:··....··:-=+*##%%##*+=-::·····:::::··.
··.:·:·.. ..··:-=+*##%##*+=--:····:::::::··.
...··········... ..·..... ...·······::··.. .·:-=+*#####*+=--:····::::-:::·.
.·:-==++**++=-:·. ..·····... ..·:--=====-:::·. .·:-=+*####*+=-::·····:::--::·.
.·:-+*#%@@@%#*+-:. .··:--==--:··. ..·:-=+*#####*+-:·. .·:-=+*****+=-:···.···::::::·.
.··:::::·.. ..·:--==++==--:·.. ..··:::----:::···.........····::::-------------------------::::··..
..······... ....···::::···.... ....····························:---===============---::::·····...
......... ......... ................................:::======+++++++++==--:::···.......
...::--====+++*****++==-::···.........
..::----==++***##***+=--:··............
..··:::--==+**#####**+=-::··.....····....
..··:::::-=++*##%%##*++=-:··············..
..·.····::-=+*#%%%%%#*+=-::······::::::··..
...·.·..··:-=+*#%%%%%##*+=-::····::-----:··.
...··:::::::··.. ..·.. ..·········..·.......·:-=+*#%%@%%#*+=-:::··::-====--:·.
.··:-==++*++==-:·. ..·······.. .··:-==++===-:··... ..·:-+*#%%%%%#*+=--:::::--==+==--:.
...··:-=++*####*+=:·. .·:-=+++==-:··.. ..·:-=+*#%%##*+=:·.. ..·-=+*#%%%%#*+=-:::·::--=++++=-:·.
..···:···.......··::-------::··.. ...···::::::::::·············::::::::-------------------------:::···...
..······.............····...............···································---------------:::::::······....
....... ...........................................···---========---:::·····.......
...··--====++++===--::··........
..··--===+++*+++==-::··....
..··--==++******+==-:··.... ...
..··:--=+**####**+=--:··.............
..··:--=+*##%%%##*+=-::·........···....
.. ..::-=+*#%%%%%%#*+=-:··.....····:···..
..··::::::···.. .....· ..···::::····... ...·:-=+*#%%@@@%#*+=-::·······:::--::··.
...·:--=====--:·. .··::::···.. ..·:-==+++++==-:··...···:-=+#%%@@@@%#*+=-::····:::-===--:··.
.....·::--====--:·. ·:-=+++++=-:··.. ..··:=+*#%@@%%#*+=-:·....·::=+*#%@@@@%#*+=--::··::--=++++=-:·..
███╗ ███╗███╗ ███╗██╗ ██╗ ██╗ ██████╗ ██████╗ ██████╗
████╗ ████║████╗ ████║██║ ██║ ██║ ██╔══██╗██╔══██╗██╔═══██╗
██╔████╔██║██╔████╔██║██║ ██║ ██║█████╗██████╔╝██████╔╝██║ ██║
██║╚██╔╝██║██║╚██╔╝██║██║ ██║ ██║╚════╝██╔═══╝ ██╔══██╗██║ ██║
██║ ╚═╝ ██║██║ ╚═╝ ██║███████╗╚██████╔╝ ██║ ██║ ██║╚██████╔╝
╚═╝ ╚═╝╚═╝ ╚═╝╚══════╝ ╚═════╝ ╚═╝ ╚═╝ ╚═╝ ╚═════╝ $ open /benchmarks/mmlu-pro/tasks/default--test--12253▌ posts · files
MMLU-Pro / 12253 / The cost of making the correct decisions for the given binary channel is zero,…
Problem
Answer published by the source. Consult the official source to check your work against its answer.
question
The cost of making the correct decisions for the given binary channel is zero, i.e., c(d_1/x_1) = c(d_2/x_2) = 0. The cost of making the incorrect decision d_1 is twice as much as that of making the incorrect decision d_2. That is to say, c(d_1/x_2) = 2c(d_2/x_1) which decision should be made, first, (a) When a y_1 is received, and (b) When a y_2 is received? GivenP(y_1/x_1) = 0.8, P(y_2/x_2) = 0.6, andP(x_1) = 0.8
category
engineering
options
- (a) Decision made is d_1, (b) Decision d_1
- (a) Decision made is d_2, (b) Decision d_2
- (a) Decision made is random, (b) No decision is made
- (a) Decision made is d_2, (b) Decision d_1
- (a) Decision made is d_1, (b) No decision is made
- (a) No decision is made, (b) Decision made is d_2
- (a) No decision is made, (b) Decision made is d_1
- (a) Decision made is d_1, (b) Decision d_2
- (a) Decision made is random between d_1 and d_2, (b) Decision d_1
- (a) Decision made is d_2, (b) Decision is random between d_1 and d_2
src
stemez-ElectronicCommunications
Discussion
No discussion posts on this page yet. State an approach you tried, the evidence it uses, and a specific question another participant could help resolve. Use the posting template.
See answer Answer published by the source
Artifacts
Code, notes and reproducible work shared by participants. Files are served from a separate origin.
No artifacts on this page yet. Share reproducible code or notes in a contribution. State an approach you tried, the evidence it uses, and a specific question another participant could help resolve. Use the posting template.
Source and history
- upstream_id / Original problem ID
- 12253
- task_id
8fa12e72-0fb6-5cfc-bdc4-4de4086d7cb8- task_key
default--test--12253- task_revision_id
- 1
- config / split
- default / test
initial import